Search results for: Intrinsic mode function.

Authors: A. Arul Lawrence Selvakumar, C. Suresh Ganandhas

Abstract:

This paper describes the study of cryptographic hash functions, one of the most important classes of primitives used in recent techniques in cryptography. The main aim is the development of recent crypt analysis hash function. We present different approaches to defining security properties more formally and present basic attack on hash function. We recall Merkle-Damgard security properties of iterated hash function. The Main aim of this paper is the development of recent techniques applicable to crypt Analysis hash function, mainly from SHA family. Recent proposed attacks an MD5 & SHA motivate a new hash function design. It is designed not only to have higher security but also to be faster than SHA-256. The performance of the new hash function is at least 30% better than that of SHA-256 in software. And it is secure against any known cryptographic attacks on hash functions.

Keywords: Crypt Analysis, cryptographic.

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Authors: Cyrille Lambert, Tatiana Kalganova, Emanuele Stomeo, Manissa Wilson

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A multi-board run-time reconfigurable (MRTR) system for evolvable hardware (EHW) is introduced with the aim to implement on hardware the bidirectional incremental evolution (BIE) method. The main features of this digital intrinsic EHW solution rely on the multi-board approach, the variable chromosome length management and the partial configuration of the reconfigurable circuit. These three features provide a high scalability to the solution. The design has been written in VHDL with the concern of not being platform dependant in order to keep a flexibility factor as high as possible. This solution helps tackling the problem of evolving complex task on digital configurable support.

Keywords: Evolvable Hardware, Evolutionary Strategy, multiboardFPGA system.

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Authors: Niloufar Ghoreishi, Ali Nekouzadeh

Abstract:

The stability of the flight during maneuvering and in response to probable perturbations is one of the most essential features of an aircraft that should be analyzed and designed for. In this study, we derived the non-linear governing equations of aircraft dynamics during the climb/descend phase and simulated a model aircraft. The corresponding force and moment dimensionless coefficients of the model and their variations with elevator angle and other relevant aerodynamic parameters were measured experimentally. The short-period mode and phugoid mode response were simulated by solving the governing equations numerically and then compared with the desired stability parameters for the particular level, category, and class of the aircraft model. To meet the target stability, a controller was designed and used. This resulted in significant improvement in the stability parameters of the flight.

Keywords: Flight stability, phugoid mode, short period mode, climb phase, damping coefficient.

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Authors: P. Jelodarian , E. Farshidi

Abstract:

In this paper, a new approach for design of a fully differential second order current mode continuous-time sigma-delta modulator is presented. For circuit implementation, square root domain (SRD) translinear loop based on floating-gate MOS transistors that operate in saturation region is employed. The modulator features, low supply voltage, low power consumption (8mW) and high dynamic range (55dB). Simulation results confirm that this design is suitable for data converters.

Keywords: Sigma-delta, current-mode, translinear loop, geometric mean, squarer/divider.

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Authors: Chun-Yao Lee, Hung-Chi Lin

Abstract:

This paper presents a signal analysis process for improving energy completeness based on the Hilbert-Huang Transform (HHT). Firstly, the vibration signal of a DC Motor obtained by employing an accelerometer is the model used to analyze the signal. Secondly, the intrinsic mode functions (IMFs) and Hilbert spectrum of the decomposed signal are obtained by applying HHT. The results of the IMFs constituent and the original signal are compared and the process of energy loss is discussed. Finally, the differences between Wavelet Transform (WT) and HHT in analyzing the signal are compared. The simulated results reveal the analysis process based on HHT is advantageous for the enhancement of energy completeness.

Keywords: Hilbert-Huang transform, Hilbert spectrum, Wavelettransform, Wavelet spectrum, DC Motor.

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Authors: Thanapiyawanit Bancha, Lu Jau-Huai

Abstract:

In this study, we developed a model to predict the temperature and the pressure variation in an internal combustion engine operated in HCCI (Homogeneous charge compression ignition) mode. HCCI operation begins from aspirating of homogeneous charge mixture through intake valve like SI (Spark ignition) engine and the premixed charge is compressed until temperature and pressure of mixture reach autoignition point like diesel engine. Combustion phase was described by double-Wiebe function. The single zone model coupled with an double-Wiebe function were performed to simulated pressure and temperature between the period of IVC (Inlet valve close) and EVO (Exhaust valve open). Mixture gas properties were implemented using STANJAN and transfer the results to main model. The model has considered the engine geometry and enables varying in fuelling, equivalence ratio, manifold temperature and pressure. The results were compared with the experiment and showed good correlation with respect to combustion phasing, pressure rise, peak pressure and temperature. This model could be adapted and use to control start of combustion for HCCI engine.

Keywords: Double-Wiebe function, HCCI, Ignition enhancer, Single zone model.

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Authors: Ismail Abubakar, Hamid Mehrabi, Reg Morton

Abstract:

Currently, extensive signal analysis is performed in order to evaluate structural health of turbomachinery blades. This approach is affected by constraints of time and the availability of qualified personnel. Thus, new approaches to blade dynamics identification that provide faster and more accurate results are sought after. Generally, modal analysis is employed in acquiring dynamic properties of a vibrating turbomachinery blade and is widely adopted in condition monitoring of blades. The analysis provides useful information on the different modes of vibration and natural frequencies by exploring different shapes that can be taken up during vibration since all mode shapes have their corresponding natural frequencies. Experimental modal testing and finite element analysis are the traditional methods used to evaluate mode shapes with limited application to real live scenario to facilitate a robust condition monitoring scheme. For a real time mode shape evaluation, rapid evaluation and low computational cost is required and traditional techniques are unsuitable. In this study, artificial neural network is developed to evaluate the mode shape of a lab scale rotating blade assembly by using result from finite element modal analysis as training data. The network performance evaluation shows that artificial neural network (ANN) is capable of mapping the correlation between natural frequencies and mode shapes. This is achieved without the need of extensive signal analysis. The approach offers advantage from the perspective that the network is able to classify mode shapes and can be employed in real time including simplicity in implementation and accuracy of the prediction. The work paves the way for further development of robust condition monitoring system that incorporates real time mode shape evaluation.

Keywords: Modal analysis, artificial neural network, mode shape, natural frequencies, pattern recognition.

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Authors: Simon B. Cooper, Stephan Bandelow, Maria L. Nute, John G. Morris, Mary E. Nevill

Abstract:

Previous research has indicated a variable effect of exercise on adolescents’ cognitive function. However, comparisons between studies are difficult to make due to differences in: the mode, intensity and duration of exercise employed; the components of cognitive function measured (and the tests used to assess them); and the timing of the cognitive function tests in relation to the exercise. Therefore, the aim of the present study was to assess the time course (10 and 60min post-exercise) of the effects of 15min intermittent exercise on cognitive function in adolescents. 45 adolescents were recruited to participate in the study and completed two main trials (exercise and resting) in a counterbalanced crossover design. Participants completed 15min of intermittent exercise (in cycles of 1 min exercise, 30s rest). A battery of computer based cognitive function tests (Stroop test, Sternberg paradigm and visual search test) were completed 30 min pre- and 10 and 60min post-exercise (to assess attention, working memory and perception respectively).The findings of the present study indicate that on the baseline level of the Stroop test, 10min following exercise response times were slower than at any other time point on either trial (trial by session time interaction, p = 0.0308). However, this slowing of responses also tended to produce enhanced accuracy 10min post-exercise on the baseline level of the Stroop test (trial by session time interaction, p = 0.0780). Similarly, on the complex level of the visual search test there was a slowing of response times 10 min post-exercise (trial by session time interaction, p = 0.0199). However, this was not coupled with an improvement in accuracy (trial by session time interaction, p = 0.2349). The mid-morning bout of exercise did not affect response times or accuracy across the morning on the Sternberg paradigm. In conclusion, the findings of the present study suggest an equivocal effect of exercise on adolescents' cognitive function. The mid-morning bout of exercise appears to cause a speed-accuracy trade off immediately following exercise on the Stroop test (participants become slower but more accurate), whilst slowing response times on the visual search test and having no effect on performance on the Sternberg paradigm. Furthermore, this work highlights the importance of the timing of the cognitive function tests relative to the exercise and the components of cognitive function examined in future studies. 

Keywords: Adolescents, cognitive function, exercise.

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Authors: Haiyan Wang

Abstract:

Being main teaching media and major source of comprehensive target language input, teacher talk plays an important role in learners' second-language acquisition. Under the trend of "learner-centered" teaching mode, some researchers think that the best teacher talk means less. But the author holds that, in Chinese second language classroom, it is not advisable to lay too much stress on the formal students' participation, which requires the teacher to say as little as possible and the student to say as much as possible. The emphasis should be put on how to raise teacher talk's quality.

Keywords: Comprehensive language input, "learner-centered" teaching mode, teacher talk, teacher talk's quality.

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Authors: Muhammad Awais Shafique, Eiji Hato, Hideki Yaginuma

Abstract:

Recently GPS data is used in a lot of studies to automatically reconstruct travel patterns for trip survey. The aim is to minimize the use of questionnaire surveys and travel diaries so as to reduce their negative effects. In this paper data acquired from GPS and accelerometer embedded in smart phones is utilized to predict the mode of transportation used by the phone carrier. For prediction, Support Vector Machine (SVM) and Adaptive boosting (AdaBoost) are employed. Moreover a unique method to improve the prediction results from these algorithms is also proposed. Results suggest that the prediction accuracy of AdaBoost after improvement is relatively better than the rest.

Keywords: Accelerometer, AdaBoost, GPS, Mode Prediction, Support vector Machine.

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Authors: K. Melouk, M. Dellakrachai

Abstract:

Analytical formula for the optical gain based on a simple parabolic-band by introducing theoretical expressions for the quantized energy is presented. The model used in this treatment take into account the effects of intraband relaxation. It is shown, as a result, that the gain for the TE mode is larger than that for TM mode and the presence of acceptor impurity increase the peak gain.

Keywords: Laser, quantum well, semiconductor, InGaAsP.

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Authors: Jenn-Yih Chen, Bean-Yin Lee, Yuan-Chuan Hsu, Jui-Cheng Lin, Kuang-Chyi Lee

Abstract:

In this paper, a sliding mode control method based on the passivity approach is proposed to control the position of surface-mounted permanent magnet synchronous motors (PMSMs). Firstly, the dynamics of a PMSM was proved to be strictly passive. The position controller with an adaptive law was used to estimate the load torque to eliminate the chattering effects associated with the conventional sliding mode controller. The stability analysis of the overall position control system was carried out by adopting the passivity theorem instead of Lyapunov-type arguments. Finally, experimental results were provided to show that the good position tracking can be obtained, and exhibit robustness in the variations of the motor parameters and load torque disturbances.

Keywords: Adaptive law, passivity theorem, permanent magnet synchronous motor, sliding mode control.

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Authors: M.Bensaada , A.Boudghene Stambouli , M.Bekhti, A. Bellar, L. Boukhris

Abstract:

This paper is a simple and systematic approaches to the design and analysis a pulse width modulation (PWM) based sliding mode controller for buck DC-DC Converters. Various aspects of the design, including the practical problems and the proposed solutions, are detailed. However, these control strategies can't compensate for large load current and input voltage variations. In this paper, a new control strategy by compromising both schemes advantages and avoiding their drawbacks is proposed, analyzed and simulated.

Keywords: Buck, DC/DC converters, sliding mode control, pulse width modulation.

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Authors: S. Sundaravalli, M. C. Majumder, G. K. Vijayaraghavan

Abstract:

The study focuses to investigate the thermal response of delaminations and develop mathematical models using numerical results to obtain the optimum heat requirement and time to identify delaminations in GLARE type of Fibre Metal Laminates (FML) in both reflection mode and through-transmission (TT) mode of step pulsed active thermography (SPAT) method in the type of nondestructive testing and evaluation (NDTE) technique. The influence of applied heat flux and time on various sizes and depth of delaminations in FML is analyzed to investigate the thermal response through numerical simulations. A finite element method (FEM) is applied to simulate SPAT through ANSYS software based on 3D transient heat transfer principle with the assumption of reflection mode and TT mode of observation individually.

The results conclude that the numerical approach based on SPAT in reflection mode is more suitable for analysing smaller size of near-surface delaminations located at the thermal stimulator side and TT mode is more suitable for analysing smaller size of deeper delaminations located far from thermal stimulator side or near thermal detector/Infrared camera side. The mathematical models provide the optimum q and T at the required MRTD to identify unidentified delamination 7 with 25015.0022W/m2 at 2.531sec and delamination 8 with 16663.3356 W/m2 at 1.37857sec in reflection mode. In TT mode, the delamination 1 with 34954W/m2 at 13.0399sec, delamination 2 with 20002.67W/m2 at 1.998sec and delamination 7 with 20010.87 W/m2 at 0.6171sec could be identified.

Keywords: Step pulsed active thermography (SPAT), NDTE, FML, Delaminations, Finite element method.

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Authors: Mahdi Kiani, Hassan Salarieh, Aria Alasty, S. Mahdi Darbandi

Abstract:

The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.

Keywords: Active magnetic bearing, three pole AMB, hybrid control, Lyapunov function.

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Authors: P. Silapan, C. Chanapromma, T. Worachak

Abstract:

This article proposes a current-mode square-rooting circuit using current follower transconductance amplifier (CTFA). The amplitude of the output current can be electronically controlled via input bias current with wide input dynamic range. The proposed circuit consists of only single CFTA. Without any matching conditions and external passive elements, the circuit is then appropriate for an IC architecture. The magnitude of the output signal is temperature-insensitive. The PSpice simulation results are depicted, and the given results agree well with the theoretical anticipation. The power consumption is approximately 1.96mW at ±1.5V supply voltages.

Keywords: CFTA, Current-mode, Square-rooting Circuit

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Authors: Ebrahim Farshidi

Abstract:

This paper presents a new circuit arrangement for a current-mode Wheatstone bridge that is suitable for low-voltage integrated circuits implementation. Compared to the other proposed circuits, this circuit features severe reduction of the elements number, low supply voltage (1V) and low power consumption (<350uW). In addition, the circuit has favorable nonlinearity error (<0.35%), operate with multiple sensors and works by single supply voltage. The circuit employs MOSFET transistors, so it can be used for standard CMOS fabrication. Simulation results by HSPICE show high performance of the circuit and confirm the validity of the proposed design technique.

Keywords: Wheatstone bridge, current-mode, low-voltage, MOS.

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Authors: Koson Pitaksuttayaprot, Winai Jaikla

Abstract:

The realization of current-mode quadrature oscillators using current controlled current conveyor transconductance amplifiers (CCCCTAs) and grounded capacitors is presented. The proposed oscillators can provide 2 sinusoidal output currents with 90º phase difference. It is enabled non-interactive dual-current control for both the condition of oscillation and the frequency of oscillation. High output impedances of the configurations enable the circuit to be cascaded without additional current buffers. The use of only grounded capacitors is ideal for integration. The circuit performances are depicted through PSpice simulations, they show good agreement to theoretical anticipation.

Keywords: Current-mode, Oscillator, Integrated circuit, CCCCTA.

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Authors: Mustafa Resa Becan

Abstract:

Sliding mode control with a fuzzy boundary layer is presented to hydraulic position control problem in this paper. A nonlinear hydraulic servomechanism which has an asymmetric cylinder is modeled and simulated first, then the proposed control scheme is applied to this model versus the conventional sliding mode control. Simulation results proved that the chattering free position control is achieved by tuning the fuzzy scaling factors properly.

Keywords: Hydraulic servomechanism, position control, sliding mode control, chattering, fuzzy boundary layer.

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Authors: Marcel Schneider, Nils Nießen

Abstract:

Microscopic simulation tool kits allow for consideration of the two processes of railway operations and the previous timetable production. Block occupation conflicts on both process levels are often solved by using defined train priorities. These conflict resolutions (dispatching decisions) generate reactionary delays to the involved trains. The sum of reactionary delays is commonly used to evaluate the quality of railway operations, which describes the timetable robustness. It is either compared to an acceptable train performance or the delays are appraised economically by linear monetary functions. It is impossible to adequately evaluate dispatching decisions without a well-founded objective function. This paper presents a new approach for the evaluation of dispatching decisions. The approach uses mode choice models and considers the behaviour of the end-customers. These models evaluate the reactionary delays in more detail and consider other competing modes of transport. The new approach pursues the coupling of a microscopic model of railway operations with the macroscopic choice mode model. At first, it will be implemented for railway operations process but it can also be used for timetable production. The evaluation considers the possibility for the customer to interchange to other transport modes. The new approach starts to look at rail and road, but it can also be extended to air travel. The result of mode choice models is the modal split. The reactions by the end-customers have an impact on the revenue of the train operating companies. Different purposes of travel have different payment reserves and tolerances towards late running. Aside from changes to revenues, longer journey times can also generate additional costs. The costs are either time- or track-specific and arise from required changes to rolling stock or train crew cycles. Only the variable values are summarised in the contribution margin, which is the base for the monetary evaluation of delays. The contribution margin is calculated for different possible solutions to the same conflict. The conflict resolution is optimised until the monetary loss becomes minimal. The iterative process therefore determines an optimum conflict resolution by monitoring the change to the contribution margin. Furthermore, a monetary value of each dispatching decision can also be derived.

Keywords: Choice of mode, monetary evaluation, railway operations, reactionary delays.

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Authors: Ma Myint Myint Aye

Abstract:

Any rotation of a 3-dimensional object can be performed by three consecutive rotations over Euler angles. Intrinsic rotations produce the same result as extrinsic rotations in transformation. Euler rotations are the movement obtained by changing one of the Euler angles while leaving the other two constant. These Euler rotations are applied in a simple two-axis gimbals set mounted on an automotives. The values of Euler angles are [π/4, π/4, π/4] radians inside the angles ranges for a given coordinate system and these actual orientations can be directly measured from these gimbals set of moving automotives but it can occur the gimbals lock in application at [π/2.24, 0, 0] radians. In order to avoid gimbals lock, the values of quaternion must be [π/4.8, π/8.2, 0, π/4.8] radians. The four-gimbals set can eliminate gimbals lock.

Keywords: Intrinsic rotations, extrinsic rotations, Euler rotations, rotation matrices, quaternion.

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Authors: Y. Madani, H. Achache, B. Boutabout

Abstract:

The purpose of this paper is to analyze numerically by the three-dimensional finite element method, using ABAQUS calculation code, the mechanical behavior of a unidirectional and multidirectional delaminated stratified composite under mechanical loading in Mode II. This study consists of the determination of the energy release rate G in mode II as well as the distribution of equivalent von Mises stresses along the damaged zone by varying several parameters such as the applied load and the delamination length. It allowed us to deduce that the high energy release rate favors delamination at the free edges of a stratified plate subjected to bending.

Keywords: Delamination, energy release rate, finite element method, stratified composite.

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Authors: Martin Leroux, Sylvain Brisebois

Abstract:

Eating a meal is among the Activities of Daily Living, but it takes a lot of time and effort for people with physical or functional limitations. Dedicated technologies are cumbersome and not portable, while general-purpose assistive robots such as wheelchair-based manipulators are too hard to control for elaborate continuous motion like eating. Eating with such devices has not previously been automated, since there existed no description of a feeding motion for uncontrolled environments. In this paper, we introduce a feeding mode for assistive manipulators, including a mathematical description of trajectories for motions that are difficult to perform manually such as gathering and scooping food at a defined/desired pace. We implement these trajectories in a sequence of movements for a semi-automated feeding mode which can be controlled with a very simple 3-button interface, allowing the user to have control over the feeding pace. Finally, we demonstrate the feeding mode with a JACO robotic arm and compare the eating speed, measured in bites per minute of three eating methods: a healthy person eating unaided, a person with upper limb limitations or disability using JACO with manual control, and a person with limitations using JACO with the feeding mode. We found that the feeding mode allows eating about 5 bites per minute, which should be sufficient to eat a meal under 30min.

Keywords: Assistive robotics, Automated feeding, Elderly care, Trajectory design, Human-Robot Interaction.

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Authors: R. Loukil, M. Chtourou, T. Damak

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In this work, we use the Fault detection and isolation and the Fault tolerant control based on sliding mode observer in order to introduce the well diagnosis of a nonlinear system. The robustness of the proposed observer for the two techniques is tested through a physical example. The results in this paper show the interaction between the Fault tolerant control and the Diagnosis procedure.

Keywords: Fault detection and isolation “FDI”, Fault tolerant control “FTC”, sliding mode observer, nonlinear system, robustness, stability.

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Authors: K. D. Mroczek

Abstract:

In the study presented institutional context is discussed in terms of companies’ entry mode choice. In contrary to many previous analyses, instead of using one or two aggregated variables, a set of eleven determinants is used to establish equity and non-equity internationalization friendly conditions. Based on secondary data, 140 countries are analyzed and grouped into clusters revealing similar framework. The range of the economies explored is wide as it covers all regions distinguished by The World Bank. The results can prove a useful alternative for operationalization of institutional variables in further research concerning entry modes or strategic management in international markets.

Keywords: Clustering, entry mode choice, institutional environment, transaction costs.

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Authors: Danijela Tuljak-Suban, Valter Suban

Abstract:

Food as perishable goods represents a specific and sensitive part in the supply chain theory, since changing physical or chemical characteristics considerably influence the approach to stock management. The most delicate phase of this process is transportation, where it becomes difficult to ensure the stable conditions which limit deterioration, since the value of the deterioration rate could be easily influenced by the mode of transportation. The fuzzy definition of variables allows one to take these variations into account. Furthermore, an appropriate choice of the defuzzification method permits one to adapt results to real conditions as far as possible. In this article those methods which take into account the relationship between the deterioration rate of perishable goods and transportation by ship will be applied with the aim of (a) minimizing the total cost function, defined as the sum of the ordering cost, holding cost, disposing cost and transportation costs, and (b) improving the supply chain sustainability by reducing environmental impact and waste disposal costs.

Keywords: Perishable goods, fuzzy reasoning, transport by ship, supply chain sustainability.

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Authors: Mary Gloria C. Njoku, Leonard A. Jason, Nicole Porter, Molly Brown

Abstract:

The objective of this study was to examine the interaction between mode of illness onset and psychiatric comorbidity on the health outcomes of persons with ME/CFS. A total of 114 individuals with ME/CFS participated in this study. Individuals completed a battery of baseline measures including the fatigue severity scale and measures of disability. Findings indicated that those with sudden illness onset had more impaired physical health functioning. In addition, among individuals with sudden onset, those without psychiatric comorbidity had greater fatigue severity and lower overall physical health than those with psychiatric comordibity. In contrast, among individuals with gradual illness onset, those with psychiatric comorbity had higher fatigue severity than those without comorbid psychiatric disorders. The health outcomes of individuals who have ME/CFS with or without psychiatric comorbidity are impacted by the mode of illness onset and this suggest that it is important to examine these factors in future research.

Keywords: Health Outcomes, ME/CFS, Mode of Illness Onset, Psychiatric Comorbidity.

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Authors: J. Fei

Abstract:

This paper presents the adaptive control scheme with sliding mode compensator for vibration control problem in the presence of disturbance. The dynamic model of the flexible cantilever beam using finite element modeling is derived. The adaptive control with sliding mode compensator using output feedback for output tracking is developed to reject the external disturbance, and to improve the tracking performance. Satisfactory simulation results verify that the effectiveness of adaptive control scheme with sliding mode compensator.

Keywords: finite element model, adaptive control, sliding modecontrol, vibration suppression

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Authors: Fan-Yong Meng

Abstract:

In this paper, we first introduce the model of games on augmenting systems with a coalition structure, which can be seen as an extension of games on augmenting systems. The core of games on augmenting systems with a coalition structure is defined, and an equivalent form is discussed. Meantime, the Shapley function for this type of games is given, and two axiomatic systems of the given Shapley function are researched. When the given games are quasi convex, the relationship between the core and the Shapley function is discussed, which does coincide as in classical case. Finally, a numerical example is given.

Keywords: Cooperative game, augmenting system, Shapley function, core.

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Authors: H. Ifassiouen, M. Guisser, H.Medromi

Abstract:

This paper presents an investigation into the design of a flight control system, using a robust sliding mode control structure, designed using the exact feedback linearization procedure of the dynamic of a small-size autonomous helicopter in hover. The robustness of the controller in the context of stabilization and trajectory tracking with respect to small body forces and air resistance on the main and tail rotor, is analytically proved using Lyapunov approach. Some simulation results are presented to illustrate the performance and robustness of such controller in the presence of small body forces and air resistance.

Keywords: Robust control, sliding mode, stability, Lyapunovapproach.

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